X' and 'Y' are the two open ends of a glass tube with a length of 1m. `NH_(3)` gas through 'X' and HCl gas through 'Y' are simultaneously allowed to enter the tube. As `NH_(3)` and HCl gases diffuse towards each other inside the tube, they meet and react to form `NH_(4)Cl()`, and as a result of which a white fume appears. where will the white fume appear first inside the tube?

Explanation

Suppose, `NH_(3)` gas first comes in contact with HCl gas after it traverses a distance of l cm from the X-end of the tube. In the same time, HCl gas moves a distance of (100-l) cm from the Y-end of the tube. Therefore, first white fume, appearing due to the formation of `NH_(4)` Cl(s) from the reaction of `NH_(3)` with HCl, will be seen at a distance of l cm from the X-end.

If `r_(1) and r_(2)` be the rate of diffusion of `NH_(3) and HCl` respectively, then
`r_(1)=(l)/(t) and r_(2)=((100-l))/(t)" "therefore (r_(1))/(r_(2))=sqrt((M_(HCl))/(N_(NH_(3))))`
or `(l)/(100-l)=sqrt((36.5)/(17)) or, (l)/(100-l)=1.465 or, l=59.43cm`
So, white fume first appears at a distance of 59.43 cm from the 'X'-end of the tube.